{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison of the Doppler and Lorentz line widths"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This comparison is computed as a function of pressure (and frequency) using Equation 9.37 in Petty (2006), A first course in Atmospheric Radiation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1170d8320>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ee7gSEVeyEbZ3ld2hqDTM1TqA7saYWcaYmyLSxtNBKZUSxhjmHZlC0+Cudody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\nE4CZWUX9A2KTR+AZJ7c5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116f5cf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set pressure and temperature.\n",
    "p  = 300.\n",
    "T  = 230.               # Kelvin\n",
    "\n",
    "# Doppler line\n",
    "v0 = 31.26e12            # 1042 cm-1 in Hz (for Ozone).\n",
    "kB = 1.3806488e-23       # Boltzmann constant\n",
    "m  = (3.*16) / 6.02e23   # Molar mass divided by Avogadro's number\n",
    "c2 = (3e8)**2            # Speed of light squared.\n",
    "aD = v0 * (2.*kB*T/(m*c2))\n",
    "\n",
    "varr = arange(-0.2,0.2,0.001)\n",
    "fD = 1./(aD*pi**0.5)*exp(-varr**2 / aD**2)\n",
    "\n",
    "# Lorentz line\n",
    "p0 = 1013.5                      # mb\n",
    "T0 = 273.15                      # K\n",
    "a0 = 0.05                         # Typical value for a0\n",
    "n  = 0.6                         # Typical value for n (I think)\n",
    "\n",
    "aL = a0 * (p/p0) * (T0/T)**n\n",
    "#varr = arange(-2,2,0.001)\n",
    "fL = (aL/pi)/(varr**2 + aL**2)\n",
    "\n",
    "plot(varr/aD,fD,varr/aL,fL)\n",
    "axis([-4,4,0,max(fD)*1.1])\n",
    "xlabel('(v-v0)/aD')\n",
    "ylabel('Normalized f(v-v0)')\n",
    "title('Doppler and Lorentz Line Shapes')\n",
    "legend(('Doppler','Lorentz'),loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Equation 9.37 from Petty(2006).\n",
    "v0      = 20.01e12                    # v0 must be in Hz.\n",
    "p       = arange(1., 1000., 1.)     # p must be in mb.\n",
    "a_ratio = 5.e-13 * v0 / p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x114ff70f0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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I04G3lh1MP/AfZL7cnuM3Wq2G27M6Ck8YkhZIWifpzqblR0u6R9K9ks5pWDUR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\nwjAzs0z+PzZXCUjJaoAKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a309b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loglog(a_ratio,p)\n",
    "xlabel('aD / aL')\n",
    "ylabel('pressure (mb)')\n",
    "title('Ratio of the Doppler and Lorentz line widths')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
